Matching Tag: covering-groups
Derivative conjecture. The representation ρ 1 ( τ ) \rho_1(\tau) ρ 1 ( τ ) ( r k , 1 ) (rk,1) ( r k , 1 ) F F F c > 1 c>1 c > 1 ρ c ( τ ) \rho_c(\tau) ρ c ( τ )
Let G G G F F F G ‾ ( n ) \overline{G}^{(n)} G ( n ) G G G Irr g e n ( G ‾ ( n ) ) \operatorname{Irr}_{\rm gen}(\overline{G}^{(n)}) Irr gen ( G ( n ) )
Let G G G Basic G \textnormal{\textsf{Basic}}_G Basic G β ∈ Basic G \beta\in\textnormal{\textsf{Basic}}_G β ∈ Basic G G ~ β \widetilde G_\beta G β
Let F F F G ~ \widetilde G G H ~ \widetilde H H Π ( G ~ ) \Pi(\widetilde G) Π ( G )
Maximal Whittaker-orbit conjecture. One has O r , n ⩽ O \mathcal{O}^{r,n}\leqslant\mathcal{O} O r , n ⩽ O O ∈ N W h max ( π ) \mathcal{O}\in\mathcal{N}_{\rm Wh}^{\rm \max}(\pi) O ∈ N Wh m a x ( π )
Let G ‾ \overline{G} G G ‾ 0 \overline{G}_0 G 0 G ‾ † = Z ( G ) ‾ ⋅ G ‾ 0 \overline{G}^\dag=\overline{Z(G)}\cdot\overline{G}_0 G † = Z ( G ) ⋅ G 0 ϕ π \phi_\pi ϕ π L L L
Let G G G σ n ( G ) \sigma_n(G) σ n ( G ) G G G
Intertwining-operator conjecture. For all 1 < l ≤ r 1<l\leq r 1 < l ≤ r M ( ζ , w ( k l ) ) M(\zeta,w_{(k^{l})}) M ( ζ , w ( k l ) ) ζ = ζ ( l ) \zeta=\zeta^{(l)} ζ = ζ ( l ) c ≥ 1 c\geq1 c ≥ 1
Let G ‾ \overline{G} G n n n Θ ( G ‾ , χ ) = π Γ − \Theta(\overline{G},\chi)=\pi_{\Gamma^-} Θ ( G , χ ) = π Γ − χ \chi χ
Let F F F ν \nu ν F F F τ ν \tau_\nu τ ν l ≥ 2 l\geq 2 l ≥ 2
Let ( GL ~ r ( n ) , GL ~ R ( n ) ) (\widetilde{\operatorname{GL}}_r^{(n)},\widetilde{\operatorname{GL}}_R^{(n)}) ( GL r ( n ) , GL R ( n ) ) n ∣ ( p ⋅ n α ) n\mid(\mathbf{p}\cdot n_\alpha) n ∣ ( p ⋅ n α )
Let G G G i s t h e s m a l l e s t n u m b e r o f p r o p e r s u b g r o u p s n e e d e d t o c o v e r is the smallest number of proper subgroups needed to cover i s t h es ma l l es t n u mb er o f p r o p er s u b g r o u p s n ee d e d t oco v er . C a l l . Call . C a l l ∗ ∗ … ** … ∗ ∗ … σ ( G / N ) … σ \sigma(G/N) … \sigma σ ( G / N ) … σ
